Design of robust gain scheduled controller using $L_2$ gain performance

Veselý, Vojtech ; Ernek, Martin

Kybernetika, Tome 54 (2018) no. 3, pp. 593-609

Abstract (VO)

This paper is devoted to robust gain scheduled PID controller design with $L_2$ performance for the linear time varying (LPV) uncertain system with polytopic uncertainties. The novel approach of robust controller design ensures that the obtained design procedure is convex with respect to both plant uncertainties (polytopic system) and gain scheduling parameters and gives less conservative results. Modified design procedure should be used to obtain a robust controller or robust switched controller (ideal, non-ideal switching) with arbitrarily switching algorithm. The effectiveness of the proposed approach is illustrated on the simulation examples.

Détail

DOI : 10.14736/kyb-2018-3-0593

Classification : 70E60, 93B36
Keywords: gain scheduled controller; Linear parameter varying systems (LPV); robust controller; switched controller; $L_2$ gain performance

Bibliographie

[1] Boyd, S., Ghaoui, L. E., al., E. Feron et: Linear Matrix Inequalities in system and control theory, volume 4. Society for Industrial and Applied Mathematics, 1994. | DOI | MR

[2] Coutinho, D., Fu, M., al., A. Trofino et: L2-gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs. Int. J, Robust Nonlinear Control 18 (2008), 1, 88-110. | DOI | MR

[3] Isidori, A.: Robust stability via \emph{$H_\infty$} methods. 2011 (last accessed 3 April 2017) DOI 

[4] Krokavec, D., Filasova, A.: On enhanced mixed \emph{$H_2/H_{\infty}$}; design conditions for control of linear time-invariant systems. In: 17th International Carpathian Control Conference (ICCC), 2016, pp. 384-389. | DOI

[5] Pfifer, H., Seiler, P.: Robustness analysis of linear parameter varying systems using integral quadratic constraints. Int. J. Robust Nonlinear Control 25 (2015), 15, 2843-2864. | DOI | MR

[6] Santarelli, K. R., Dahleh, M. A.: L2 gain stability of switched output feedback controllers for a class of lti systems. IEEE Trans. Automat. Control 54 (2009), 7, 1504-1514. | DOI | MR

[7] Sato, M.: Gain-scheduled output-feedback controllers depending solely on scheduling parameters via parameter-dependent Lyapunov functions. Automatica 47 (2011), 12, 2786-2790. | DOI | MR

[8] Sato, M., Peaucelle, D.: Gain-scheduled output-feedback controllers using inexact scheduling parameters for continuous-time LPV systems. Automatica 49 (2013), 4, 1019-1025. | DOI | MR

[9] Shamma, J. S., Athans, M.: Analysis of gain scheduled control for nonlinear plants. IEEE Trans. Automat. Control 35 (1990), 8, 898-907. | DOI | MR | Zbl

[10] Toth, R.: Modeling and Identification of Linear Parameter-Varying Systems. Springer-Verlag, Berlin, Heidelberg 2010. | MR

[11] Veselý, V., Ilka, A.: Gain-scheduled PID controller design. J. Process Control 23 (2013), 8, 1141-1148.

[12] Veselý, V., Ilka, A.: Design of robust gain-scheduled PI controllers. J. Franklin Inst. 352 (2015), 4, 1476-1494. | DOI | MR

[13] Veselý, V., Ilka, A.: Robust switched controller design for nonlinear continuous systems. IFAC-PapersOnLine 48 (2015), 11, 1068-1073. | DOI

[14] Veselý, V., Ilka, A.: Novel approach to switched controller design for linear continuous-time systems. Asian J. Control 18 (2016), 4, 1365-1375. | DOI | MR

[15] Veselý, V., Rosinová, D.: Robust pid-psd controller design: Bmi approach. Asian J. Control 15 (2013), 2, 469-478. | DOI | MR

[16] Wang, S., Seiler, P.: Gain scheduled active power control for wind turbines. In: 32nd ASME Wind Energy Symposium, AIAA SciTech Forum, 2014. | DOI

[17] Wu, F., Yang, X. H., al., A. Packard et: Induced l2-norm control for lpv systems with bounded parameter variation rates. Int. J. Robust Nonlinear Control 6 (1996), 9-10, 983-998. | DOI | MR